Hwk10SolnFinDrtSp06

# Hwk10SolnFinDrtSp06 - HW 10 Solutions Question 1 Uno...

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HW 10 Solutions Question 1. Uno Pizzeria, a leading national fast-casual restaurant chain, recently completed a comprehensive study in association with the Hotel School to determine, based on a variety of factors, how much total sales a server will bring in during any one period. Since the analysis was very advanced and the data set involved over 20 predictors, management wanted a smaller, executive summary type analysis: please use the attached data file which shows each servers average check per person as well as three predictors of their ability to sell: 1) MTBI Score (a personality measure); 2) Height; and 3) An index of the length and quality of the individual’s previous work experience. Data appears in Hwk10Q1DatSp06. A) Plot the dependent variable against each of the three independent variables and briefly describe the relationships. X-Data Avgerage Check Per Person 80 70 60 50 40 30 20 10 0 30 25 20 15 10 5 0 Variable Experience Quality Index MBTI Score Height (in inches) Scatterplot of Avgerage Che vs MBTI  Score, Height (in i, Experience Q

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H ADM 201 Homework X Spring 2006 Avgerage Check Per Person 60 45 30 15 0 75 70 65 60 55 30 20 10 0 60 45 30 15 0 30 20 10 0 MBTI Score Height (in inches) Experience Quality Index Scatterplot of Avgerage Che vs MBTI  Score, Height (in i, Experience Q All 3 relationships appear to be linear and positively related. Height appears to have the largest slope. This tells us that as the height (in inches) changes, the average check per person will increase by a greater amount then the increase from MBTI or Experience Quality Index. B) Fit a multiple linear regression model to the data using all three predictor variables and determine the estimated regression equation. Regression Analysis: Avgerage Che versus MBTI Score, Height (in i, ... The regression equation is Avgerage Check Per Person = - 25.7 + 0.0605 MBTI Score + 0.470 Height (in inches) + 0.253 Experience Quality Index Predictor Coef SE Coef T P Constant -25.700 5.142 -5.00 0.000 MBTI Score 0.06048 0.02363 2.56 0.013 Height (in inches) 0.47017 0.09772 4.81 0.000 Experience Quality Index 0.25268 0.03311 7.63 0.000 S = 0.839366 R-Sq = 98.7% R-Sq(adj) = 98.6% Analysis of Variance Source DF SS MS F P Regression 3 3010.3 1003.4 1424.23 0.000 Residual Error 56 39.5 0.7 Total 59 3049.7 2
H ADM 201 Homework X Spring 2006 Source DF Seq SS MBTI Score 1 2778.6 Height (in inches) 1 190.7 Experience Quality Index 1 41.0 Unusual Observations Avgerage Check MBTI Per Obs Score Person Fit SE Fit Residual St Resid 25 8.0 4.440 2.454 0.191 1.986 2.43R 34 6.0 8.920 7.718 0.406 1.202 1.64 X 39 10.0 2.680 5.068 0.279 -2.388 -3.02R 42 7.0 2.440 2.745 0.436 -0.305 -0.43 X R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large influence. The estimated regression equation is: Avgerage Check Per Person = - 25.7 + 0.0605 MBTI Score + 0.470 Height (in inches)+ 0.253 Experience Quality Index C) Give the ANOVA table for regression and perform a significance test of the null hypothesis H 0 1 2 3 0 : β β β = = = vs H a : Not H o . Compute test statistic and p-value (yes, compute them; they are easily checked on the output). Carefully state your conclusions Analysis of Variance Source DF SS MS F P Regression 3 3010.3 1003.4 1424.23 0.000 Residual Error 56 39.5 0.7 Total 59 3049.7 Source DF Seq SS MBTI Score 1 2778.6

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• Spring '06
• RLLOYD
• Regression Analysis, MBTI score, Source Regression Residual, Regression Residual Error, Variance Source Regression, Experience Quality Index

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